from PIL import Image import pytesseract

Load the image to extract text

image_path = '/mnt/data/17317333478539p4bdujg.jpg' text = pytesseract.image_to_string(Image.open(image_path))

text'Nagi 2 loge (x*-2)\n''Nagi 2 loge (x*-2)\n'successThe equation extracted from the image appears to be:

$\log_2 x = \log_2 (x^2 - 2)$

Let's solve for $x$.

Step 1: Remove the logarithms

Since the logarithms have the same base, we can equate the arguments: $x = x^2 - 2$

Step 2: Rearrange the equation

Rearranging the terms: $x^2 - x - 2 = 0$

Step 3: Factorize the quadratic

$(x - 2)(x + 1) = 0$

Step 4: Solve for $x$

The solutions are: $x = 2 \quad \text{or} \quad x = -1$

Step 5: Check for extraneous solutions

Logarithms are only defined for positive values, so $x > 0$. Therefore, $x = -1$ is not valid.

The only solution is: $\boxed{x = 2}$

Would you like a detailed explanation or verification of any step?

Here are 5 related questions:

1. How do you solve logarithmic equations with different bases?
2. Can you explain why logarithms are undefined for non-positive numbers?
3. How do you solve a quadratic equation if it cannot be factored easily?
4. What happens when the bases of the logarithms are not the same?
5. How can you verify solutions of equations involving logarithms?

Tip: Always check the domain of a logarithmic equation before solving it!